Consensus and dissention: A measure of ordinal dispersion

A new measure of dispersion is introduced as a representation of consensus (agreement) and dissention (disagreement). Building on the generally accepted Shannon entropy, this measure utilizes a probability distribution and the distance between categories to produce a value spanning the unit interval. The measure is applied to the Likert scale (or any ordinal scale) to determine degrees of consensus or agreement. Using this measure, data on ordinal scales can be given a value of dispersion that is both logically and theoretically sound.